# Full text of "Treatise On Analysis Vol-Ii"

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```xiv       NOTATION

T                                               one-dimensional torus: 14.2

AG0), AO)                                  modulus function on a group: 14.3

modG(w), mod(w)                          modulus  of an automorphism of G:

14.3

Qp                                             field of p-adic numbers: 14.3, Problem 6

/b                                               average of/over a fibre: 14.4, Problem 2

/*i * #2 * '"' * A*                         convolution of n measures: 14.5

MC (X)                                       space of measures with compact support :

14.7

\$                                              centralization of a measure: 14.7, Prob-

lem 6
/* * /, M * *f» f* V>> /* V                convolution of a measure and a function:

14.8

f*g9f**g                                convolution of two functions: 14.10

SpA(X), Sp(jc)                               spectrum of an element x of an algebra

A: 15.2

p(x)                                           spectral radius of x: 15.2

X(A)                                         spectrum of an algebra A: 15.3

^                                               Gelfand transformation: 15.3

M?p(jji\ Jf *(/i), H*(/i), H°°(^)         Hardy spaces; 15.3, Problem 15

x*                                              adjoint (in an algebra with involution):

15.4

II u || 2                                                  Hilbert-Schmidt norm: 15.4

^                                                        involution in Mc(G): 15.4

^f2(E)                                               algebra of  Hilbert-Schmidt operators:

15.4

P(x), pA(x)                                   (p(x*x))i/2: 15.4, Problem 18

U(x), UA(x)                                 regular  representation  of a  complete

Hilbert algebra: 15.8

H(A)                                         space of hermitian characters: 15.9

M^(u)                                        multiplication by the class of u: 15.10

%C(K)                                        space of bounded universally measurable

complex-valued functions on K: 15.10

#^0                             (jy-x|*)^0foralljt: 15.11

f(N)                                         function of a normal operator: 15.11

H1/2                                           square root of a positive hermitian oper-

ator: 15.11

abs(T)                                        absolute value of an operator:  15.11,

Problem 6

trace   of  a   nuclear   operator:   15.11,
Problem 7e) real-valued /z-
```